Existence of strong solutions for It\^o's stochastic equations via approximations. Revisited

By István Gyöngy, Nicolai V. Krylov. 2021

151 citations recorded by the source corpus.

Given strong uniqueness for an It\^o's stochastic equation, we prove that its solution can beconstructed on"any"probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\mathbb{R}^{d}$ and in domains in $\mathbb{R}^{d}$ are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of"tamed Euler approximations"for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate exponential moments.

View Paper: https://www.semanticscholar.org/paper/0e6e8130d144cb44aa244835bf561e9b515041d4